Niles Johnson, Donald Yau
Published 2022-05-17Version 1
We show that each of the three $K$-theory multifunctors from small permutative categories to $\mathcal{G}_*$-categories, $\mathcal{G}_*$-simplicial sets, and connective spectra, is an equivalence of homotopy theories. For each of these $K$-theory multifunctors, we describe an explicit homotopy inverse functor. As a separate application of our general results about pointed diagram categories, we observe that the right-induced homotopy theory of Bohmann-Osorno $\mathcal{E}_*$-categories is equivalent to the homotopy theory of pointed simplicial categories.
An equivalence between enriched $\infty$-categories and $\infty$-categories with weak action
An $\infty$-categorical localisation functor for diagrams of simplicial sets
Univalence in Simplicial Sets
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